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Microangiopathy (also known as microvascular disease, small vessel disease (SVD) or microvascular dysfunction) is a disease of the microvessels, small blood vessels in the microcirculation. [1] It can be contrasted to macroangiopathies such as atherosclerosis , where large and medium-sized arteries (e.g., aorta , carotid and coronary arteries ...
Some aspects can be traced as far back as F. L. Hitchcock in 1928, [1] but it was L. R. Tucker who developed for third-order tensors the general Tucker decomposition in the 1960s, [2] [3] [4] further advocated by L. De Lathauwer et al. [5] in their Multilinear SVD work that employs the power method, or advocated by Vasilescu and Terzopoulos ...
Tensor-CURT decomposition [6] is a generalization of matrix-CUR decomposition. Formally, a CURT tensor approximation of a tensor A is three matrices and a (core-)tensor C, R, T and U such that C is made from columns of A, R is made from rows of A, T is made from tubes of A and that the product U(C,R,T) (where the ,,-th entry of it is ′, ′, ′ ′, ′, ′, ′, ′, ′) closely ...
Top: The action of M, indicated by its effect on the unit disc D and the two canonical unit vectors e 1 and e 2. Left: The action of V ⁎, a rotation, on D, e 1, and e 2. Bottom: The action of Σ, a scaling by the singular values σ 1 horizontally and σ 2 vertically.
Named after the Dutch mathematician Bartel Leendert van der Waerden, the Van der Waerden test is a statistical test that k population distribution functions are equal. The Van der Waerden test converts the ranks from a standard Kruskal-Wallis test to quantiles of the standard normal distribution (details given below).
There are two types of angiopathy: macroangiopathy and microangiopathy. [2] In macroangiopathy, atherosclerosis and a resultant blood clot forms on the large blood vessels, sticks to the vessel walls, and blocks the flow of blood. Macroangiopathy in the heart is coronary artery disease; in the brain, it is cerebrovascular disease.
In diseases such as hemolytic uremic syndrome, disseminated intravascular coagulation, thrombotic thrombocytopenic purpura, and malignant hypertension, the endothelial layer of small vessels is damaged with resulting fibrin deposition and platelet aggregation.
Thm.3.3 The absolute values of all elements in the inverse matrix (A −1) are at most the inverse σ n −1 (A). [2]: Thm.3.3 Intuitively, if σ n (A) is small, then the rows of A are "almost" linearly dependent. If it is σ n (A) = 0, then the rows of A are linearly dependent and A is not invertible.